© 2018. The American Astronomical Society. All rights reserved.. Splashback refers to the process of matter that is accreting onto a dark matter halo reaching its first orbital apocenter and turning around in its orbit. The clustercentric radius at which this process occurs, rsp, defines a halo boundary that is connected to the dynamics of the cluster. A rapid decline in the halo profile is expected near rsp. We measure the galaxy number density and weak lensing mass profiles around redMaPPer galaxy clusters in the first-year Dark Energy Survey (DES) data. For a cluster sample with mean M200mmass ≈2.5 × 1014Mo, we find strong evidence of a splashback-like steepening of the galaxy density profile and measure rsp= 1.13 ± 0.07 h-1Mpc, consistent with the earlier Sloan Digital Sky Survey measurements of More et al. and Baxter et al. Moreover, our weak lensing measurement demonstrates for the first time the existence of a splashback-like steepening of the matter profile of galaxy clusters. We measure rsp= 1.34 ± 0.21 h-1Mpc from the weak lensing data, in good agreement with our galaxy density measurements. For different cluster and galaxy samples, we find that, consistent with ΛCDM simulations, rspscales with R200mand does not evolve with redshift over the redshift range of 0.3-0.6. We also find that potential systematic effects associated with the redMaPPer algorithm may impact the location of rsp. We discuss the progress needed to understand the systematic uncertainties and fully exploit forthcoming data from DES and future surveys, emphasizing the importance of more realistic mock catalogs and independent cluster samples.